Bitcoin gold in a nutshell.

What is Bitcoin Gold?
Bitcoin Gold is the brainchild of Jack Liao and is launching as a hard fork of Bitcoin. The goal of BTG is to become a better gold than Bitcoin. The chief way they have decided to do this is trying to solve miner centralization through a proof-of-work change.
Changing proof-of-work is generally going to require a hard fork and BTG has decided to go that route. The proof-of-work that they’ve chosen is Equihash, a memory-hard algorithm that’s fairly ASIC resistant and also used by ZCash. The idea is to give mining back to the users who can start using CPUs and GPUs to mine.

What’s so special about ASIC resistance?
ASICs are Application Specific Integrated Circuits. They’re different from CPUs in that they do only one thing, but they do it really, really well.
Bitcoin mining is currently completely dominated by ASICs, mostly produced by Bitmain, Bitfury and Canaan. This is largely due to the proof-of-work function (SHA256) being reasonably simple and not requiring much RAM. Equihash, on the other hand, is a pretty complex hashing function and requires a lot of RAM to perform. That means it’s much more expensive to produce ASICs for Equihash and the speed gain isn’t nearly as much.
To give you an idea, a normal CPU can mine SHA256 at around 5–10 MH/s. An ASIC can mine SHA256 at around 5–10 TH/s, or about 1 million times more work per second than a CPU can. By comparison, a normal CPU can mine Equihash at around 10–30 H/s, where as specialized equipment can do something like 1000–3000 H/s, or about 100 times more work per second.
In other words, the playing field is a lot more level with Equihash than SHA256 due to the ASIC-resistance. Of course, it’s hard to know how much economics would change if Equihash were to become as profitable, but suffice it to say that the efficiency gain would still be much less than SHA256.